Answer: 1/9
Step-by-step explanation:
Total number of cards = 6
Probability = required outcome/ all possible outcome
number of kings=4
number of jack=1
Probability of drawing a king = 4/6
probability of drawing a jack = 1/6
Probability of drawing a king and then a jack is p(king and jack) = p(king) × p(jack) = 4/6 × 1/6 = 4/36
= 1/9
Answer:
1/9
thats all
Step-by-step explanation:
A book on the clearance rack was marked down 65% from $21.95. Approximately, how much was the book discounted?
Answer:
$7.6825
Step-by-step explanation:
65%=0.65
0.65*21.95=14.2675
21.95-14.2675=7.6825
Answer:
7.6825
Step-by-step explanation:
Ted likes to run long distances. He can run
20 km start text, space, k, m, end text in
95 minutes. He wants to know how many kilometers
(k)left parenthesis, k, right parenthesis he will go if he runs at the same pace for
285 minutes
Answer:
Step-by-step explanation:
20 km to 95 minutes = x km to 285 minutes
20 / 95 = x / 285.....cross multiply
(95)(x) = (20)(285)
95x = 5700
x = 5700/95
x = 60 km <======
If a pair of jeans cost 45 dollars before the sale and the sale is taking 9 dollars off of the original price what was the percent taken off?
Answer:
20%
Step-by-step explanation:
A pair of jeans cost $45 before the sale.
The sale is taking $9 off of the original price.
Then
$45 - 100%
$9 - x%
Write a proportion:
[tex]\dfrac{45}{9}=\dfrac{100}{x}[/tex]
Cross multiply:
[tex]45\cdot x=9\cdot 100\\ \\45x=900\\ \\x=\dfrac{900}{45}\\ \\x=20\%[/tex]
Answer:
The sale price is $46.75
Step-by-step explanation:
The Ferris wheel has a radius of 70 feet. The distance between the wheel and the ground is 4 feet. The rectangular coordinate system shown has its origin on the ground directly below the center of the wheel. Write the equation of the circular wheel. (JUSTIFY)
Show your work. i will give brainliest.
Answer:
The equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
Step-by-step explanation:
Given :
Radius of Ferris wheel r = 70 feet.
The distance between the wheel and the ground = 4 feet.
Also, the rectangular coordinate system shown has its origin on the ground directly below the center of the wheel.
So the x coordinate of center of wheel must be 0 , and y coordinate = 70 + 4 = 74
Thus, Coordinates of center = (0,74)
The equation of circle is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Now center (h,k) = (0,74) and r = 70 , we get
[tex]x^2+(y-74)^2=(70)^2[/tex]
Hence, the equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
MNOP is a parallelogram. U is any point on side OP. Show that ar( MUN)= ar ( Δ △ PUM)+ar( UNO) △
Answer:
The Proof is below.
Step-by-step explanation:
Given:
[]MNOP is a Parallelogram
U is any point on side OP
To Show:
ar(Δ MUN)= ar ( Δ PUM)+ar (Δ UNO)
Proof:
Theorem:
If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.
If they have same altitude, they will lie between the same parallels.
Hence the area of the triangle will be equal to half that of the parallelogram.
Area of Parallelogram will be twice of Area of Triangle
∴ [tex]\textrm{Area of Parallelogram MNOP}=2\times (area\ of\ Triangle\ MUN)[/tex].............( 1 )
Also,
[tex]\textrm{Area of Parallelogram MNOP}=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
Substituting equation 1 we get
[tex]2\times Ar(MUN)=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
[tex]2\times Ar(MUN)-Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]
[tex]Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]...........Proved
Ramona spend 8 hours making picture frames if each picture frame takes her 1/4 of hour to make how many picture frame does Ramona have?
1. Which equation shows a non-proportional
relationship?
A y=-2x
By= 2X
x
Cy=2x+ 0
Dy=2x + 2
Answer:
Option D. [tex]y=2x+2[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
case A) we have
[tex]y=-2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=-2
This equation represent a proportional relationship
case B) we have
[tex]y=2x[/tex]
Is a equation of the form [tex]y=kx[/tex]
The value of k=2
This equation represent a proportional relationship
case C) we have
[tex]y=-2x+0[/tex]
The line passes through the origin, because the y-intercept is b=0
This equation represent a proportional relationship
case D) we have
[tex]y=2x+2[/tex]
The line not passes through the origin, because the y-intercept is not equal to zero (b=2)
This equation not represent a proportional relationship
At Ashley's Hats, 75% of the 84 hats are baseball caps. How many baseball caps are there?
Answer:
63
Step-by-step explanation:
85 * .75 = 63 hats
x^2-5x=14 solve for x
Answer:
x=7, -2.
Step-by-step explanation:
x^2-5x=14
x^2-5x-14=0
factor out the trinomial,
(x-7)(x+2)=0
zero property,
x-7=0, x+2=0,
x=0+7=7,
x=0-2=-2
Answer:
x = - 2, x = 7
Step-by-step explanation:
Given
x² - 5x = 14 ( subtract 14 from both sides )
x² - 5x - 14 = 0 ← in standard form
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)
The factors are - 7 and + 2, since
- 7 × 2 = - 14 and - 7 + 2 = - 5, thus
(x - 7)(x + 2) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 7 = 0 ⇒ x = 7
WILL GIVE BRAINLIEST IF CORRECT! 25 PTS
Which statement is true about the graph of this equation?
y + 4 = 4(x + 1)
A.
The graph is a line that goes through the points (1,-4) and (0,0).
B.
The graph is a line that goes through the points (1,4) and (2,8).
C.
The graph is a line that goes through the points (-4,-1) and (-3,-3).
D.
The graph is a line that goes through the points (4,1) and (5,5).
Answer:45x-5 is the answer
Step-by-step explanation:
(4,1) and 5,5 add them both
Answer:
B.) The graph is a line that goes through the points (1,4) and (2,8).
Step-by-step explanation:
1.) (4) + 4 = 4((1) +1)
2.) 8 = 4 + 4
3.) 8 = 8 --> Correct
4.) (8) + 4 = 4((2) + 1)
5.) 12 = 8 + 4
6.) 12 = 12 --> Correct
Tony makes a phone call at a pay phone. The charge is 25 cents for the first four minutes,and 19 cents for each additional minute. Tony has $2.10 in change in his pocket. Write an inequality that can be used to find m, the maximum number of whole minutes he can talk on the phone
Use the following figure to answer the question.
∠ 1 and ∠ 2 are supplementary angles.
True
False
Answer:
True
Step-by-step explanation:
Because angles on a straight line are supplementary and these anglea <1 and <2 are supplementary angles
Answer: True
Step-by-step explanation:
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
X + 10y = 29
x - y = 7
Answer:
x = 9, y = 2
Step-by-step explanation:
Given the 2 equations
x + 10y = 29 → (1)
x - y = 7 → (2)
Subtracting (2) from (1) term by term will eliminate the term in x
(x - x) + (10y - (- y)) = (29 - 7), that is
11y = 22 ( divide both sides by 11 )
y = 2
Substitute y = 2 in either of the 2 equations
Substituting in (2)
x - 2 = 7 ( add 2 to both sides )
x = 9
how many times can 7 go into 50
Answer:
7 without going over
Step-by-step explanation:
The number 7 can go into 50 a total of 7 times with 1 remainder.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The number 7 can go into 50 a total of 7 times because 50 / 7 = 7 with 1 remainder.
To understand this, consider that when you divide 50 by 7, you are trying to find out how many groups of 7 can be created from 50. Since 50 is a multiple of 7 (50 is divisible by 7 with 1 remainder), there will be an integer number of groups. In this case, that integer is 7, so 7 groups of 7 can be created from 50.
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Solve the following system of equations using the substitution method. x=2y2x+5y=9
Answer:
x=2, y=1. (2, 1).
Step-by-step explanation:
x=2y
2x+5y=9
-------------
2(2y)+5y=9
4y+5y=9
9y=9
y=9/9
y=1
x=2(1)=2
The length of a rectangle is 5 centimeters less than its width What are the dimensions of the rectangle if its area is 66 square centimeters?
The length of the rectangle is
The width of the rectangle is
Answer:
length of rectangle=6cm
width of rectangle=11cm
Step-by-step explanation:
let, width of rectangle=x
length of rectangle=x-5
area of rectangle=[tex]length\times(width)[/tex]
given area of rectangle=66
so 66=[tex]x\times(x-5)[/tex]
66=x^2-5x
x^2-11x+6x-66=0
x(x-11)+6(x-11)=0
(x+6)(x-11)=0
x=-6,11
here x=11 is acceptable
length of rectangle=x-5=11-5=6cm
length of rectangle=6cm
width of rectangle=11cm answer
?? “solve the missing elements for each problem. use 3.14 for area
Answer:
Problem 4:
Radius = 11 cm.
Circumference = 69.08 cm.
Problem 5:
Radius = 14 mm.
Circumference = 87.92 mm.
Problem 6:
Radius = 9 inches.
Circumference = 56.52 inches.
Problem 7:
Diameter = 32 ft.
Circumference = 100.48 ft.
Problem 8:
Diameter = 26 yards.
Circumference = 81.64 yards.
Problem 9:
Diameter = 12 cm.
Circumference = 37.68 cm.
Step-by-step explanation:
Problem 4:
Given:
Diameter GH = 22 cm
We need to find the radius EF and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius EF = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 22 = 11 \ cm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 22 = 69.08\ cm[/tex]
Hence Radius = 11 cm
Circumference = 69.08 cm.
Problem 5:
Given:
Diameter OP = 28 mm
We need to find the radius MN and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius MN = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 28 = 14 \ mm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 28 = 87.92\ mm[/tex]
Hence Radius = 14 mm
Circumference = 87.92 mm.
Problem 6:
Given:
Diameter EF = 18 inches
We need to find the radius CD and Circumference of the circle.
Now radius is given by half of the diameter
Also Circumference is given by π times diameter.
Radius CD = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 18 = 9 \ in[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 18 = 56.52\ in[/tex]
Hence Radius = 9 inches.
Circumference = 56.52 inches.
Problem 7:
Given:
Radius GH = 16 ft
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter KJ = [tex]2 \times radius = 2 \times 16 = 32 \ ft[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 32 = 100.48\ ft[/tex]
Hence Diameter = 32 ft.
Circumference = 100.48 ft.
Problem 8:
Given:
Radius LM = 13 yards
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter NO = [tex]2 \times radius = 2 \times 13 = 26 \ yards[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 26 = 81.64\ yards[/tex]
Hence Diameter = 26 yards.
Circumference = 81.64 yards.
Problem 9:
Given:
Radius NO = 6 cm
We need to find the Diameter CD and Circumference of the circle.
Now Diameter is given by twice the radius.
Also Circumference is given by π times diameter.
Diameter PQ = [tex]2 \times radius = 2 \times 6 = 12 \ cm[/tex]
Circumference = [tex]\pi \times Diameter = 3.14 \times 12 = 37.68\ cm[/tex]
Hence Diameter = 12 cm.
Circumference = 37.68 cm.
What is the slope of the line represented by the equation y= -1/2x+1/4
Answer:
-1/2
Step-by-step explanation:
The format your equation in is called slope-intercept form:
y=mx+b
m stands for slope, the slope basically determines how much the line is tilted. b stands for the y intercept, the y intercept is when the line intercepts with the y axis.
Your equation is:
y= -1/2x+1/4
y= m x+ b
Home city bank pays 5% interest compounded quarterly on regular savings accounts. Miguel cardosa deposited 1000 for 1 year. He made no other deposits or withdrawals. How much interest did he earn during the year.
Answer:
The interest earned was $50.95
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=1\ year\\ P=\$1,000\\ r=5\%=5/100=0.05\\n=4[/tex]
substitute in the formula above
[tex]A=1,000(1+\frac{0.05}{4})^{4*1}[/tex]
[tex]A=1,000(1.0125)^{4}[/tex]
[tex]A=\$1,050.95[/tex]
Find the interest earned I
we know that
[tex]I=A-P[/tex]
substitute the values
[tex]I=\$1,050.95-\$1,000=\$50.95[/tex]
What's 286 divided by 20??
Thanks if you help! :)
Answer:
14.3
Step-by-step explanation:
percent: 14.3%
decimal: 14.3
fraction: 14 3/10
Answer:
I got 143/10 ;-;
But as a decimal it's 143.0 and percent is 14.3%
For what value of R does the equation have a solution of X = 9.5?
7 (5x - R) + 3r = 173.5
Show how you got your answer step-by-step.
Answer:
r=39.75
Step-by-step explanation:
7(5*9.5-R)+3r=173.5
7(47.5-R)+3r=173.5
332.5-7R+3r=173.5
332.5-4r=173.5
4r=332.5-173.5
4r=159
r=159/4
r=39.75
Step-by-step explanation:
7 (5x - R) + 3r = 173.5
let x = 9.5 as given
solve for R
substitute the value of x=9.5 into the equation:
7 (5 * 9.5 - R) + 3R = 173.5
7 (47.5 - R) + 3R = 173.5 expand
332.5 - 7R + 3R = 173.5 combine similar terms
332.5 - 173.5 = 7R - 3R simplify
159 = 4R divide 4 on each side
R = 159/4 simplify
R = 39.75
Force moved 350 boxes from the old school to the new school. Then, she moved 160 more. There are 220 boxes left to move. How many boxes needed moved to begin with?
Answer:
730
Step-by-step explanation:
Answer:
350+160+220 = 730
Step-by-step explanation:
There were 730 boxes. After moving 350 boxes out of 730 boxes, there were left 380 boxes. Again after moving 160 boxes out of 380 boxes, there were remained 220 boxes.
yyyeeeeeeeee
1-2k-2k=5
Answer:
k=-1
Step-by-step explanation:
1-2k-2k=5
1-4k=5
4k=1-5
4k=-4
k=-4/4
k=-1
Which expression represents 8 less than two times X?
OA) 2x - 8
OB) 8 - 2x
OC) 8x - 2
OD) 2-8x
Answer:
Therefore the expression is option A)
[tex]2x-8[/tex]
Step-by-step explanation:
Given:
Statement as ' 8 less than two times X'
To Find :
Expression for the statement
'8 less than two times X'
Solution:
[tex]Two\ times\ 'x'\ means=2\times x[/tex]
Now 8 less than two times X means Subtract 8 from '2x'
[tex]2x-8[/tex]
Therefore the expression is option A)
[tex]2x-8[/tex]
A force of 200 N is exerted on
an object of mass 40 kg that is
located on a sheet of perfectly
smooth ice. Calculate the
acceleration of the object.
The acceleration of the object is 5 m/s^2
Step-by-step explanation:
Given
Mass of object = m = 40 kg
Force = F = 200 N
Newton's 2nd law states that:
[tex]F = ma[/tex]
As we have to find the acceleration
[tex]a = \frac{F}{m}[/tex]
Putting the values
[tex]a = \frac{200}{40}\\a = 5\ ms^{-2}[/tex]
The acceleration of the object is 5 m/s^2
Keywords: Force, acceleration
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To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Using the given force of 200 N and mass of 40 kg, we can determine that the acceleration of the object is 5 m/s^2.
Explanation:To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
First, we need to determine the net force acting on the object. In this case, it is given as 200 N.Next, we need to determine the mass of the object, which is given as 40 kg.Using the formula: acceleration = net force / mass, we can substitute the given values to find the acceleration.Substituting the values, we get: acceleration = 200 N / 40 kg = 5 m/s^2.Therefore, the acceleration of the object is 5 m/s^2.
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What's x for 12x+1=4x+9
Nevermind someone already answered it.
For similar triangles, the side lengths are proportional. So, you can write a proportion relating the two pairs of vertical and horizontal side lengths. For the line y = 2x, a triangle can be drawn 2 units up and 1 unit right from the origin.
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The corresponding vertical sides are y and 2
The corresponding horizontal lines are x and 1
so
The proportion is equal to
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
solve and explain how you got your answer
-3(c-1) = 33
Answer:
Step-by-step explanation:
-3(c-1) = 33
c - 1 = 33/ -3
c -1 = -11
c = -11 +1
c = -10
Answer:
-10
Step-by-step explanation:
-3 (c-1 ) = 33
Divide both sides by -3
c-1 = -11
Add 1 to both sides
c = -10
Given: △ABC, AB=5 sqrt 2 m∠A=45°, m∠C=30° Find: BC and AC will give brainliest!!! By the way the answer is not 5 and 3.66
Answer:
Therefore,
[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]
Step-by-step explanation:
Consider a Δ ABC with
m∠ A = 45°
m∠ C = 30°
AB = c = 5√2
To Find:
BC = a = ?
AC = c = ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°[/tex]
We know in a Triangle Sine Rule Says that,
In Δ ABC,
[tex]\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}[/tex]
substituting the given values we get
[tex]\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}[/tex]
∴ [tex]\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units[/tex]
Similarly for 'b',
[tex]\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\[/tex]
Therefore,
[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]
By using the Law of Sines, side BC of the triangle is found to be approximately 10 m, and AC is approximately 8.66 m. These calculations take into account the given lengths and angles of triangle ABC.
Explanation:To find the lengths of sides BC and AC in triangle ABC with given angles and side AB, we will employ trigonometry and the properties of triangles. Since the sum of the angles in any triangle is 180 degrees, we know that m∠B = 180° - 45° - 30° = 105°. With this information, we can use the Law of Sines, which states:
[tex]\(\frac{AB}{\sin(C)} = \frac{BC}{\sin(A)} = \frac{AC}{\sin(B)}\)[/tex]
From the given, AB = 5√2 m, m∠A = 45°, and m∠C = 30°, we know that:
[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{BC}{\sin(45°)}\)[/tex]
[tex]Knowing \ that\ \(\sin(30 ) = 0.5\) and \(\sin(45) = \frac{\sqrt{2}}{2}\), we can find BC:[/tex]
[tex]BC = \(\frac{5\sqrt{2}}{0.5} \times \frac{\sqrt{2}}{2}\) = 5√2 \times \sqrt{2} = 10 m[/tex]
Now, to find AC, we set up the ratio:
[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{AC}{\sin(105°)}\)[/tex]
Solving for AC, we get:
[tex]AC = 5\sqrt{2} \times \frac{\sin(105°)}{0.5}[/tex]
Since \(\sin(105°)\) is not a standard angle, we can use the sine sum identity where [tex]\(\sin(105) = \sin(60 + 45\),[/tex]which gives us:
[tex]AC = 10 \times (\(\frac{\sqrt{3}}{2}\times\frac{\sqrt{2}}{2} + \frac{1}{2}\times\frac{\sqrt{2}}{2}\)) = 10 \times (\(\frac{\sqrt{6} + \sqrt{2}}{4}\))[/tex]
AC ≈ 8.66 m
Does somebody know how to do this?
Answer:
Total length of running track is 371.24 m .
Step-by-step explanation:
Total running track = Running track around straight region + running track around curved region.
Running track around straight region = 2 × length of straight region
= 2×82 m
= 164 m
Running track around curved region = 2 × length of curved region
= 2 × π × radius of curved region
= 2 × 3.14 × 33 m
= 207.24 m
Therefore , total length of running track = 164 + 207.24 m
= 371.24 m